Properties

Label 1155.2.i.c.76.15
Level $1155$
Weight $2$
Character 1155.76
Analytic conductor $9.223$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1155,2,Mod(76,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.i (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{16} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.15
Root \(1.86824 + 0.357358i\) of defining polynomial
Character \(\chi\) \(=\) 1155.76
Dual form 1155.2.i.c.76.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.60278i q^{2} -1.00000i q^{3} -4.77447 q^{4} +1.00000i q^{5} +2.60278 q^{6} +(-2.60278 + 0.474903i) q^{7} -7.22133i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+2.60278i q^{2} -1.00000i q^{3} -4.77447 q^{4} +1.00000i q^{5} +2.60278 q^{6} +(-2.60278 + 0.474903i) q^{7} -7.22133i q^{8} -1.00000 q^{9} -2.60278 q^{10} +(3.23607 + 0.726543i) q^{11} +4.77447i q^{12} -6.07163 q^{13} +(-1.23607 - 6.77447i) q^{14} +1.00000 q^{15} +9.24660 q^{16} -4.27913 q^{17} -2.60278i q^{18} +2.82604 q^{19} -4.77447i q^{20} +(0.474903 + 2.60278i) q^{21} +(-1.89103 + 8.42278i) q^{22} +5.77447 q^{23} -7.22133 q^{24} -1.00000 q^{25} -15.8031i q^{26} +1.00000i q^{27} +(12.4269 - 2.26741i) q^{28} -6.49479i q^{29} +2.60278i q^{30} -2.66550i q^{31} +9.62422i q^{32} +(0.726543 - 3.23607i) q^{33} -11.1376i q^{34} +(-0.474903 - 2.60278i) q^{35} +4.77447 q^{36} +2.66550 q^{37} +7.35557i q^{38} +6.07163i q^{39} +7.22133 q^{40} +8.37103 q^{41} +(-6.77447 + 1.23607i) q^{42} -11.9794i q^{43} +(-15.4505 - 3.46885i) q^{44} -1.00000i q^{45} +15.0297i q^{46} -12.6655i q^{47} -9.24660i q^{48} +(6.54893 - 2.47214i) q^{49} -2.60278i q^{50} +4.27913i q^{51} +28.9888 q^{52} -13.1055 q^{53} -2.60278 q^{54} +(-0.726543 + 3.23607i) q^{55} +(3.42943 + 18.7955i) q^{56} -2.82604i q^{57} +16.9045 q^{58} +4.89103i q^{59} -4.77447 q^{60} -7.86414 q^{61} +6.93771 q^{62} +(2.60278 - 0.474903i) q^{63} -6.55653 q^{64} -6.07163i q^{65} +(8.42278 + 1.89103i) q^{66} +2.92320 q^{67} +20.4306 q^{68} -5.77447i q^{69} +(6.77447 - 1.23607i) q^{70} -11.1376 q^{71} +7.22133i q^{72} -4.53482 q^{73} +6.93771i q^{74} +1.00000i q^{75} -13.4929 q^{76} +(-8.76781 - 0.354213i) q^{77} -15.8031 q^{78} +7.42122i q^{79} +9.24660i q^{80} +1.00000 q^{81} +21.7879i q^{82} +9.31722 q^{83} +(-2.26741 - 12.4269i) q^{84} -4.27913i q^{85} +31.1798 q^{86} -6.49479 q^{87} +(5.24660 - 23.3687i) q^{88} +0.418895i q^{89} +2.60278 q^{90} +(15.8031 - 2.88344i) q^{91} -27.5700 q^{92} -2.66550 q^{93} +32.9655 q^{94} +2.82604i q^{95} +9.62422 q^{96} +2.43997i q^{97} +(6.43443 + 17.0454i) q^{98} +(-3.23607 - 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 24 q^{4} - 16 q^{9} + 16 q^{11} + 16 q^{14} + 16 q^{15} + 24 q^{16} + 40 q^{23} - 16 q^{25} + 24 q^{36} - 40 q^{37} - 56 q^{42} - 24 q^{44} + 8 q^{53} + 8 q^{56} + 72 q^{58} - 24 q^{60} + 8 q^{64} + 80 q^{67} + 56 q^{70} - 24 q^{71} - 16 q^{78} + 16 q^{81} - 8 q^{86} - 40 q^{88} + 16 q^{91} - 160 q^{92} + 40 q^{93} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.60278i 1.84044i 0.391397 + 0.920222i \(0.371992\pi\)
−0.391397 + 0.920222i \(0.628008\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −4.77447 −2.38723
\(5\) 1.00000i 0.447214i
\(6\) 2.60278 1.06258
\(7\) −2.60278 + 0.474903i −0.983759 + 0.179496i
\(8\) 7.22133i 2.55313i
\(9\) −1.00000 −0.333333
\(10\) −2.60278 −0.823072
\(11\) 3.23607 + 0.726543i 0.975711 + 0.219061i
\(12\) 4.77447i 1.37827i
\(13\) −6.07163 −1.68397 −0.841984 0.539502i \(-0.818612\pi\)
−0.841984 + 0.539502i \(0.818612\pi\)
\(14\) −1.23607 6.77447i −0.330353 1.81055i
\(15\) 1.00000 0.258199
\(16\) 9.24660 2.31165
\(17\) −4.27913 −1.03784 −0.518921 0.854822i \(-0.673666\pi\)
−0.518921 + 0.854822i \(0.673666\pi\)
\(18\) 2.60278i 0.613481i
\(19\) 2.82604 0.648339 0.324169 0.945999i \(-0.394915\pi\)
0.324169 + 0.945999i \(0.394915\pi\)
\(20\) 4.77447i 1.06760i
\(21\) 0.474903 + 2.60278i 0.103632 + 0.567973i
\(22\) −1.89103 + 8.42278i −0.403169 + 1.79574i
\(23\) 5.77447 1.20406 0.602030 0.798474i \(-0.294359\pi\)
0.602030 + 0.798474i \(0.294359\pi\)
\(24\) −7.22133 −1.47405
\(25\) −1.00000 −0.200000
\(26\) 15.8031i 3.09925i
\(27\) 1.00000i 0.192450i
\(28\) 12.4269 2.26741i 2.34846 0.428500i
\(29\) 6.49479i 1.20605i −0.797722 0.603026i \(-0.793962\pi\)
0.797722 0.603026i \(-0.206038\pi\)
\(30\) 2.60278i 0.475201i
\(31\) 2.66550i 0.478738i −0.970929 0.239369i \(-0.923060\pi\)
0.970929 0.239369i \(-0.0769405\pi\)
\(32\) 9.62422i 1.70134i
\(33\) 0.726543 3.23607i 0.126475 0.563327i
\(34\) 11.1376i 1.91009i
\(35\) −0.474903 2.60278i −0.0802732 0.439950i
\(36\) 4.77447 0.795745
\(37\) 2.66550 0.438205 0.219103 0.975702i \(-0.429687\pi\)
0.219103 + 0.975702i \(0.429687\pi\)
\(38\) 7.35557i 1.19323i
\(39\) 6.07163i 0.972240i
\(40\) 7.22133 1.14179
\(41\) 8.37103 1.30733 0.653667 0.756782i \(-0.273230\pi\)
0.653667 + 0.756782i \(0.273230\pi\)
\(42\) −6.77447 + 1.23607i −1.04532 + 0.190729i
\(43\) 11.9794i 1.82684i −0.407015 0.913421i \(-0.633430\pi\)
0.407015 0.913421i \(-0.366570\pi\)
\(44\) −15.4505 3.46885i −2.32925 0.522949i
\(45\) 1.00000i 0.149071i
\(46\) 15.0297i 2.21600i
\(47\) 12.6655i 1.84745i −0.383053 0.923726i \(-0.625127\pi\)
0.383053 0.923726i \(-0.374873\pi\)
\(48\) 9.24660i 1.33463i
\(49\) 6.54893 2.47214i 0.935562 0.353162i
\(50\) 2.60278i 0.368089i
\(51\) 4.27913i 0.599198i
\(52\) 28.9888 4.02003
\(53\) −13.1055 −1.80017 −0.900087 0.435710i \(-0.856497\pi\)
−0.900087 + 0.435710i \(0.856497\pi\)
\(54\) −2.60278 −0.354194
\(55\) −0.726543 + 3.23607i −0.0979670 + 0.436351i
\(56\) 3.42943 + 18.7955i 0.458277 + 2.51166i
\(57\) 2.82604i 0.374319i
\(58\) 16.9045 2.21967
\(59\) 4.89103i 0.636758i 0.947964 + 0.318379i \(0.103138\pi\)
−0.947964 + 0.318379i \(0.896862\pi\)
\(60\) −4.77447 −0.616381
\(61\) −7.86414 −1.00690 −0.503450 0.864024i \(-0.667936\pi\)
−0.503450 + 0.864024i \(0.667936\pi\)
\(62\) 6.93771 0.881090
\(63\) 2.60278 0.474903i 0.327920 0.0598321i
\(64\) −6.55653 −0.819566
\(65\) 6.07163i 0.753094i
\(66\) 8.42278 + 1.89103i 1.03677 + 0.232770i
\(67\) 2.92320 0.357126 0.178563 0.983928i \(-0.442855\pi\)
0.178563 + 0.983928i \(0.442855\pi\)
\(68\) 20.4306 2.47757
\(69\) 5.77447i 0.695164i
\(70\) 6.77447 1.23607i 0.809704 0.147738i
\(71\) −11.1376 −1.32179 −0.660897 0.750477i \(-0.729824\pi\)
−0.660897 + 0.750477i \(0.729824\pi\)
\(72\) 7.22133i 0.851042i
\(73\) −4.53482 −0.530760 −0.265380 0.964144i \(-0.585497\pi\)
−0.265380 + 0.964144i \(0.585497\pi\)
\(74\) 6.93771i 0.806492i
\(75\) 1.00000i 0.115470i
\(76\) −13.4929 −1.54774
\(77\) −8.76781 0.354213i −0.999185 0.0403663i
\(78\) −15.8031 −1.78935
\(79\) 7.42122i 0.834952i 0.908688 + 0.417476i \(0.137085\pi\)
−0.908688 + 0.417476i \(0.862915\pi\)
\(80\) 9.24660i 1.03380i
\(81\) 1.00000 0.111111
\(82\) 21.7879i 2.40608i
\(83\) 9.31722 1.02270 0.511349 0.859373i \(-0.329146\pi\)
0.511349 + 0.859373i \(0.329146\pi\)
\(84\) −2.26741 12.4269i −0.247395 1.35588i
\(85\) 4.27913i 0.464137i
\(86\) 31.1798 3.36220
\(87\) −6.49479 −0.696314
\(88\) 5.24660 23.3687i 0.559290 2.49111i
\(89\) 0.418895i 0.0444028i 0.999754 + 0.0222014i \(0.00706750\pi\)
−0.999754 + 0.0222014i \(0.992932\pi\)
\(90\) 2.60278 0.274357
\(91\) 15.8031 2.88344i 1.65662 0.302266i
\(92\) −27.5700 −2.87437
\(93\) −2.66550 −0.276399
\(94\) 32.9655 3.40013
\(95\) 2.82604i 0.289946i
\(96\) 9.62422 0.982268
\(97\) 2.43997i 0.247741i 0.992298 + 0.123870i \(0.0395307\pi\)
−0.992298 + 0.123870i \(0.960469\pi\)
\(98\) 6.43443 + 17.0454i 0.649975 + 1.72185i
\(99\) −3.23607 0.726543i −0.325237 0.0730203i
\(100\) 4.77447 0.477447
\(101\) 6.15537 0.612482 0.306241 0.951954i \(-0.400929\pi\)
0.306241 + 0.951954i \(0.400929\pi\)
\(102\) −11.1376 −1.10279
\(103\) 13.1300i 1.29374i −0.762600 0.646871i \(-0.776077\pi\)
0.762600 0.646871i \(-0.223923\pi\)
\(104\) 43.8453i 4.29938i
\(105\) −2.60278 + 0.474903i −0.254005 + 0.0463458i
\(106\) 34.1106i 3.31312i
\(107\) 10.1032i 0.976710i 0.872645 + 0.488355i \(0.162403\pi\)
−0.872645 + 0.488355i \(0.837597\pi\)
\(108\) 4.77447i 0.459423i
\(109\) 2.21566i 0.212222i 0.994354 + 0.106111i \(0.0338398\pi\)
−0.994354 + 0.106111i \(0.966160\pi\)
\(110\) −8.42278 1.89103i −0.803080 0.180303i
\(111\) 2.66550i 0.252998i
\(112\) −24.0669 + 4.39124i −2.27411 + 0.414933i
\(113\) −6.00759 −0.565147 −0.282573 0.959246i \(-0.591188\pi\)
−0.282573 + 0.959246i \(0.591188\pi\)
\(114\) 7.35557 0.688912
\(115\) 5.77447i 0.538472i
\(116\) 31.0091i 2.87913i
\(117\) 6.07163 0.561323
\(118\) −12.7303 −1.17192
\(119\) 11.1376 2.03217i 1.02099 0.186289i
\(120\) 7.22133i 0.659214i
\(121\) 9.94427 + 4.70228i 0.904025 + 0.427480i
\(122\) 20.4686i 1.85314i
\(123\) 8.37103i 0.754790i
\(124\) 12.7263i 1.14286i
\(125\) 1.00000i 0.0894427i
\(126\) 1.23607 + 6.77447i 0.110118 + 0.603518i
\(127\) 1.01017i 0.0896377i −0.998995 0.0448188i \(-0.985729\pi\)
0.998995 0.0448188i \(-0.0142711\pi\)
\(128\) 2.18323i 0.192972i
\(129\) −11.9794 −1.05473
\(130\) 15.8031 1.38603
\(131\) −20.3387 −1.77700 −0.888502 0.458873i \(-0.848253\pi\)
−0.888502 + 0.458873i \(0.848253\pi\)
\(132\) −3.46885 + 15.4505i −0.301925 + 1.34479i
\(133\) −7.35557 + 1.34210i −0.637809 + 0.116375i
\(134\) 7.60845i 0.657270i
\(135\) −1.00000 −0.0860663
\(136\) 30.9010i 2.64974i
\(137\) −9.63435 −0.823118 −0.411559 0.911383i \(-0.635016\pi\)
−0.411559 + 0.911383i \(0.635016\pi\)
\(138\) 15.0297 1.27941
\(139\) −3.08173 −0.261389 −0.130695 0.991423i \(-0.541721\pi\)
−0.130695 + 0.991423i \(0.541721\pi\)
\(140\) 2.26741 + 12.4269i 0.191631 + 1.05026i
\(141\) −12.6655 −1.06663
\(142\) 28.9888i 2.43269i
\(143\) −19.6482 4.41130i −1.64307 0.368891i
\(144\) −9.24660 −0.770550
\(145\) 6.49479 0.539363
\(146\) 11.8031i 0.976834i
\(147\) −2.47214 6.54893i −0.203898 0.540147i
\(148\) −12.7263 −1.04610
\(149\) 16.8456i 1.38004i −0.723790 0.690021i \(-0.757601\pi\)
0.723790 0.690021i \(-0.242399\pi\)
\(150\) −2.60278 −0.212516
\(151\) 16.7907i 1.36641i −0.730227 0.683204i \(-0.760586\pi\)
0.730227 0.683204i \(-0.239414\pi\)
\(152\) 20.4078i 1.65529i
\(153\) 4.27913 0.345947
\(154\) 0.921939 22.8207i 0.0742919 1.83894i
\(155\) 2.66550 0.214098
\(156\) 28.9888i 2.32096i
\(157\) 5.04463i 0.402605i −0.979529 0.201303i \(-0.935483\pi\)
0.979529 0.201303i \(-0.0645174\pi\)
\(158\) −19.3158 −1.53668
\(159\) 13.1055i 1.03933i
\(160\) −9.62422 −0.760861
\(161\) −15.0297 + 2.74231i −1.18450 + 0.216124i
\(162\) 2.60278i 0.204494i
\(163\) −16.9045 −1.32406 −0.662032 0.749476i \(-0.730306\pi\)
−0.662032 + 0.749476i \(0.730306\pi\)
\(164\) −39.9672 −3.12091
\(165\) 3.23607 + 0.726543i 0.251928 + 0.0565613i
\(166\) 24.2507i 1.88222i
\(167\) −6.32283 −0.489275 −0.244638 0.969615i \(-0.578669\pi\)
−0.244638 + 0.969615i \(0.578669\pi\)
\(168\) 18.7955 3.42943i 1.45011 0.264586i
\(169\) 23.8647 1.83575
\(170\) 11.1376 0.854218
\(171\) −2.82604 −0.216113
\(172\) 57.1953i 4.36110i
\(173\) 8.78248 0.667719 0.333860 0.942623i \(-0.391649\pi\)
0.333860 + 0.942623i \(0.391649\pi\)
\(174\) 16.9045i 1.28153i
\(175\) 2.60278 0.474903i 0.196752 0.0358993i
\(176\) 29.9226 + 6.71805i 2.25550 + 0.506392i
\(177\) 4.89103 0.367632
\(178\) −1.09029 −0.0817208
\(179\) −11.1224 −0.831331 −0.415665 0.909518i \(-0.636451\pi\)
−0.415665 + 0.909518i \(0.636451\pi\)
\(180\) 4.77447i 0.355868i
\(181\) 8.49321i 0.631295i −0.948877 0.315648i \(-0.897778\pi\)
0.948877 0.315648i \(-0.102222\pi\)
\(182\) 7.50495 + 41.1321i 0.556304 + 3.04891i
\(183\) 7.86414i 0.581334i
\(184\) 41.6993i 3.07412i
\(185\) 2.66550i 0.195971i
\(186\) 6.93771i 0.508697i
\(187\) −13.8476 3.10897i −1.01263 0.227350i
\(188\) 60.4710i 4.41030i
\(189\) −0.474903 2.60278i −0.0345441 0.189324i
\(190\) −7.35557 −0.533629
\(191\) −25.1189 −1.81754 −0.908771 0.417294i \(-0.862978\pi\)
−0.908771 + 0.417294i \(0.862978\pi\)
\(192\) 6.55653i 0.473177i
\(193\) 5.20556i 0.374705i −0.982293 0.187352i \(-0.940009\pi\)
0.982293 0.187352i \(-0.0599906\pi\)
\(194\) −6.35069 −0.455953
\(195\) −6.07163 −0.434799
\(196\) −31.2677 + 11.8031i −2.23341 + 0.843081i
\(197\) 14.1068i 1.00507i −0.864557 0.502536i \(-0.832401\pi\)
0.864557 0.502536i \(-0.167599\pi\)
\(198\) 1.89103 8.42278i 0.134390 0.598581i
\(199\) 0.217938i 0.0154492i 0.999970 + 0.00772462i \(0.00245885\pi\)
−0.999970 + 0.00772462i \(0.997541\pi\)
\(200\) 7.22133i 0.510625i
\(201\) 2.92320i 0.206187i
\(202\) 16.0211i 1.12724i
\(203\) 3.08439 + 16.9045i 0.216482 + 1.18646i
\(204\) 20.4306i 1.43043i
\(205\) 8.37103i 0.584658i
\(206\) 34.1746 2.38106
\(207\) −5.77447 −0.401353
\(208\) −56.1420 −3.89275
\(209\) 9.14527 + 2.05324i 0.632592 + 0.142026i
\(210\) −1.23607 6.77447i −0.0852968 0.467483i
\(211\) 26.5392i 1.82703i 0.406802 + 0.913516i \(0.366644\pi\)
−0.406802 + 0.913516i \(0.633356\pi\)
\(212\) 62.5716 4.29744
\(213\) 11.1376i 0.763138i
\(214\) −26.2963 −1.79758
\(215\) 11.9794 0.816989
\(216\) 7.22133 0.491349
\(217\) 1.26585 + 6.93771i 0.0859317 + 0.470962i
\(218\) −5.76687 −0.390582
\(219\) 4.53482i 0.306434i
\(220\) 3.46885 15.4505i 0.233870 1.04167i
\(221\) 25.9813 1.74769
\(222\) 6.93771 0.465628
\(223\) 1.96783i 0.131776i 0.997827 + 0.0658878i \(0.0209879\pi\)
−0.997827 + 0.0658878i \(0.979012\pi\)
\(224\) −4.57057 25.0497i −0.305384 1.67371i
\(225\) 1.00000 0.0666667
\(226\) 15.6365i 1.04012i
\(227\) 1.60527 0.106546 0.0532729 0.998580i \(-0.483035\pi\)
0.0532729 + 0.998580i \(0.483035\pi\)
\(228\) 13.4929i 0.893586i
\(229\) 9.05222i 0.598188i 0.954224 + 0.299094i \(0.0966844\pi\)
−0.954224 + 0.299094i \(0.903316\pi\)
\(230\) −15.0297 −0.991027
\(231\) −0.354213 + 8.76781i −0.0233055 + 0.576880i
\(232\) −46.9010 −3.07920
\(233\) 7.41312i 0.485650i −0.970070 0.242825i \(-0.921926\pi\)
0.970070 0.242825i \(-0.0780741\pi\)
\(234\) 15.8031i 1.03308i
\(235\) 12.6655 0.826206
\(236\) 23.3521i 1.52009i
\(237\) 7.42122 0.482060
\(238\) 5.28929 + 28.9888i 0.342854 + 1.87907i
\(239\) 7.67691i 0.496578i 0.968686 + 0.248289i \(0.0798682\pi\)
−0.968686 + 0.248289i \(0.920132\pi\)
\(240\) 9.24660 0.596866
\(241\) 13.6044 0.876340 0.438170 0.898892i \(-0.355627\pi\)
0.438170 + 0.898892i \(0.355627\pi\)
\(242\) −12.2390 + 25.8828i −0.786753 + 1.66381i
\(243\) 1.00000i 0.0641500i
\(244\) 37.5471 2.40371
\(245\) 2.47214 + 6.54893i 0.157939 + 0.418396i
\(246\) 21.7879 1.38915
\(247\) −17.1587 −1.09178
\(248\) −19.2484 −1.22228
\(249\) 9.31722i 0.590455i
\(250\) 2.60278 0.164614
\(251\) 21.9567i 1.38590i −0.720987 0.692948i \(-0.756311\pi\)
0.720987 0.692948i \(-0.243689\pi\)
\(252\) −12.4269 + 2.26741i −0.782821 + 0.142833i
\(253\) 18.6866 + 4.19540i 1.17481 + 0.263762i
\(254\) 2.62924 0.164973
\(255\) −4.27913 −0.267969
\(256\) −18.7955 −1.17472
\(257\) 3.99649i 0.249294i −0.992201 0.124647i \(-0.960220\pi\)
0.992201 0.124647i \(-0.0397799\pi\)
\(258\) 31.1798i 1.94117i
\(259\) −6.93771 + 1.26585i −0.431088 + 0.0786563i
\(260\) 28.9888i 1.79781i
\(261\) 6.49479i 0.402017i
\(262\) 52.9373i 3.27047i
\(263\) 10.4192i 0.642477i 0.946998 + 0.321238i \(0.104099\pi\)
−0.946998 + 0.321238i \(0.895901\pi\)
\(264\) −23.3687 5.24660i −1.43824 0.322906i
\(265\) 13.1055i 0.805062i
\(266\) −3.49318 19.1449i −0.214181 1.17385i
\(267\) 0.418895 0.0256360
\(268\) −13.9567 −0.852543
\(269\) 22.2279i 1.35526i −0.735403 0.677630i \(-0.763007\pi\)
0.735403 0.677630i \(-0.236993\pi\)
\(270\) 2.60278i 0.158400i
\(271\) −4.55819 −0.276890 −0.138445 0.990370i \(-0.544210\pi\)
−0.138445 + 0.990370i \(0.544210\pi\)
\(272\) −39.5674 −2.39913
\(273\) −2.88344 15.8031i −0.174514 0.956449i
\(274\) 25.0761i 1.51490i
\(275\) −3.23607 0.726543i −0.195142 0.0438122i
\(276\) 27.5700i 1.65952i
\(277\) 18.0744i 1.08599i −0.839737 0.542993i \(-0.817291\pi\)
0.839737 0.542993i \(-0.182709\pi\)
\(278\) 8.02107i 0.481072i
\(279\) 2.66550i 0.159579i
\(280\) −18.7955 + 3.42943i −1.12325 + 0.204948i
\(281\) 12.7654i 0.761517i −0.924674 0.380759i \(-0.875663\pi\)
0.924674 0.380759i \(-0.124337\pi\)
\(282\) 32.9655i 1.96307i
\(283\) −12.7384 −0.757218 −0.378609 0.925557i \(-0.623597\pi\)
−0.378609 + 0.925557i \(0.623597\pi\)
\(284\) 53.1763 3.15543
\(285\) 2.82604 0.167400
\(286\) 11.4816 51.1400i 0.678924 3.02397i
\(287\) −21.7879 + 3.97542i −1.28610 + 0.234662i
\(288\) 9.62422i 0.567113i
\(289\) 1.31094 0.0771144
\(290\) 16.9045i 0.992667i
\(291\) 2.43997 0.143033
\(292\) 21.6513 1.26705
\(293\) 14.0114 0.818555 0.409278 0.912410i \(-0.365781\pi\)
0.409278 + 0.912410i \(0.365781\pi\)
\(294\) 17.0454 6.43443i 0.994110 0.375263i
\(295\) −4.89103 −0.284767
\(296\) 19.2484i 1.11879i
\(297\) −0.726543 + 3.23607i −0.0421583 + 0.187776i
\(298\) 43.8453 2.53989
\(299\) −35.0605 −2.02760
\(300\) 4.77447i 0.275654i
\(301\) 5.68906 + 31.1798i 0.327912 + 1.79717i
\(302\) 43.7025 2.51480
\(303\) 6.15537i 0.353617i
\(304\) 26.1313 1.49873
\(305\) 7.86414i 0.450299i
\(306\) 11.1376i 0.636696i
\(307\) −8.27920 −0.472519 −0.236259 0.971690i \(-0.575922\pi\)
−0.236259 + 0.971690i \(0.575922\pi\)
\(308\) 41.8616 + 1.69118i 2.38529 + 0.0963638i
\(309\) −13.1300 −0.746942
\(310\) 6.93771i 0.394035i
\(311\) 11.0297i 0.625436i −0.949846 0.312718i \(-0.898761\pi\)
0.949846 0.312718i \(-0.101239\pi\)
\(312\) 43.8453 2.48225
\(313\) 7.27776i 0.411363i 0.978619 + 0.205682i \(0.0659411\pi\)
−0.978619 + 0.205682i \(0.934059\pi\)
\(314\) 13.1301 0.740972
\(315\) 0.474903 + 2.60278i 0.0267577 + 0.146650i
\(316\) 35.4324i 1.99323i
\(317\) 8.69007 0.488083 0.244042 0.969765i \(-0.421527\pi\)
0.244042 + 0.969765i \(0.421527\pi\)
\(318\) −34.1106 −1.91283
\(319\) 4.71874 21.0176i 0.264199 1.17676i
\(320\) 6.55653i 0.366521i
\(321\) 10.1032 0.563904
\(322\) −7.13763 39.1189i −0.397765 2.18001i
\(323\) −12.0930 −0.672873
\(324\) −4.77447 −0.265248
\(325\) 6.07163 0.336794
\(326\) 43.9987i 2.43686i
\(327\) 2.21566 0.122526
\(328\) 60.4499i 3.33779i
\(329\) 6.01488 + 32.9655i 0.331611 + 1.81745i
\(330\) −1.89103 + 8.42278i −0.104098 + 0.463659i
\(331\) 17.2380 0.947486 0.473743 0.880663i \(-0.342903\pi\)
0.473743 + 0.880663i \(0.342903\pi\)
\(332\) −44.4848 −2.44142
\(333\) −2.66550 −0.146068
\(334\) 16.4569i 0.900484i
\(335\) 2.92320i 0.159712i
\(336\) 4.39124 + 24.0669i 0.239562 + 1.31296i
\(337\) 5.09846i 0.277731i −0.990311 0.138865i \(-0.955654\pi\)
0.990311 0.138865i \(-0.0443455\pi\)
\(338\) 62.1147i 3.37859i
\(339\) 6.00759i 0.326288i
\(340\) 20.4306i 1.10800i
\(341\) 1.93660 8.62573i 0.104873 0.467110i
\(342\) 7.35557i 0.397744i
\(343\) −15.8714 + 9.54454i −0.856976 + 0.515356i
\(344\) −86.5073 −4.66416
\(345\) 5.77447 0.310887
\(346\) 22.8589i 1.22890i
\(347\) 4.63022i 0.248563i −0.992247 0.124282i \(-0.960337\pi\)
0.992247 0.124282i \(-0.0396626\pi\)
\(348\) 31.0091 1.66226
\(349\) 14.2418 0.762347 0.381173 0.924504i \(-0.375520\pi\)
0.381173 + 0.924504i \(0.375520\pi\)
\(350\) 1.23607 + 6.77447i 0.0660706 + 0.362111i
\(351\) 6.07163i 0.324080i
\(352\) −6.99241 + 31.1446i −0.372696 + 1.66001i
\(353\) 12.7755i 0.679971i −0.940431 0.339985i \(-0.889578\pi\)
0.940431 0.339985i \(-0.110422\pi\)
\(354\) 12.7303i 0.676607i
\(355\) 11.1376i 0.591124i
\(356\) 2.00000i 0.106000i
\(357\) −2.03217 11.1376i −0.107554 0.589466i
\(358\) 28.9493i 1.53002i
\(359\) 16.6836i 0.880527i −0.897869 0.440263i \(-0.854885\pi\)
0.897869 0.440263i \(-0.145115\pi\)
\(360\) −7.22133 −0.380598
\(361\) −11.0135 −0.579657
\(362\) 22.1060 1.16186
\(363\) 4.70228 9.94427i 0.246806 0.521939i
\(364\) −75.4515 + 13.7669i −3.95474 + 0.721580i
\(365\) 4.53482i 0.237363i
\(366\) −20.4686 −1.06991
\(367\) 28.2279i 1.47348i 0.676174 + 0.736742i \(0.263637\pi\)
−0.676174 + 0.736742i \(0.736363\pi\)
\(368\) 53.3942 2.78337
\(369\) −8.37103 −0.435778
\(370\) −6.93771 −0.360674
\(371\) 34.1106 6.22382i 1.77094 0.323125i
\(372\) 12.7263 0.659830
\(373\) 9.90424i 0.512822i 0.966568 + 0.256411i \(0.0825400\pi\)
−0.966568 + 0.256411i \(0.917460\pi\)
\(374\) 8.09196 36.0421i 0.418426 1.86369i
\(375\) −1.00000 −0.0516398
\(376\) −91.4617 −4.71678
\(377\) 39.4340i 2.03095i
\(378\) 6.77447 1.23607i 0.348441 0.0635765i
\(379\) 25.7464 1.32250 0.661251 0.750164i \(-0.270026\pi\)
0.661251 + 0.750164i \(0.270026\pi\)
\(380\) 13.4929i 0.692169i
\(381\) −1.01017 −0.0517523
\(382\) 65.3791i 3.34509i
\(383\) 10.5119i 0.537133i 0.963261 + 0.268567i \(0.0865499\pi\)
−0.963261 + 0.268567i \(0.913450\pi\)
\(384\) 2.18323 0.111413
\(385\) 0.354213 8.76781i 0.0180524 0.446849i
\(386\) 13.5489 0.689623
\(387\) 11.9794i 0.608948i
\(388\) 11.6495i 0.591416i
\(389\) 17.4410 0.884293 0.442146 0.896943i \(-0.354217\pi\)
0.442146 + 0.896943i \(0.354217\pi\)
\(390\) 15.8031i 0.800223i
\(391\) −24.7097 −1.24962
\(392\) −17.8521 47.2920i −0.901668 2.38861i
\(393\) 20.3387i 1.02595i
\(394\) 36.7170 1.84978
\(395\) −7.42122 −0.373402
\(396\) 15.4505 + 3.46885i 0.776417 + 0.174316i
\(397\) 12.0059i 0.602558i 0.953536 + 0.301279i \(0.0974135\pi\)
−0.953536 + 0.301279i \(0.902586\pi\)
\(398\) −0.567246 −0.0284335
\(399\) 1.34210 + 7.35557i 0.0671889 + 0.368239i
\(400\) −9.24660 −0.462330
\(401\) −14.5860 −0.728388 −0.364194 0.931323i \(-0.618656\pi\)
−0.364194 + 0.931323i \(0.618656\pi\)
\(402\) 7.60845 0.379475
\(403\) 16.1839i 0.806179i
\(404\) −29.3886 −1.46214
\(405\) 1.00000i 0.0496904i
\(406\) −43.9987 + 8.02800i −2.18362 + 0.398423i
\(407\) 8.62573 + 1.93660i 0.427562 + 0.0959936i
\(408\) 30.9010 1.52983
\(409\) 8.50150 0.420372 0.210186 0.977661i \(-0.432593\pi\)
0.210186 + 0.977661i \(0.432593\pi\)
\(410\) −21.7879 −1.07603
\(411\) 9.63435i 0.475227i
\(412\) 62.6889i 3.08846i
\(413\) −2.32276 12.7303i −0.114296 0.626416i
\(414\) 15.0297i 0.738668i
\(415\) 9.31722i 0.457365i
\(416\) 58.4347i 2.86500i
\(417\) 3.08173i 0.150913i
\(418\) −5.34414 + 23.8031i −0.261390 + 1.16425i
\(419\) 24.4400i 1.19397i 0.802252 + 0.596985i \(0.203635\pi\)
−0.802252 + 0.596985i \(0.796365\pi\)
\(420\) 12.4269 2.26741i 0.606370 0.110638i
\(421\) −22.8513 −1.11370 −0.556851 0.830612i \(-0.687991\pi\)
−0.556851 + 0.830612i \(0.687991\pi\)
\(422\) −69.0757 −3.36255
\(423\) 12.6655i 0.615818i
\(424\) 94.6389i 4.59607i
\(425\) 4.27913 0.207568
\(426\) −28.9888 −1.40451
\(427\) 20.4686 3.73470i 0.990546 0.180735i
\(428\) 48.2373i 2.33164i
\(429\) −4.41130 + 19.6482i −0.212980 + 0.948625i
\(430\) 31.1798i 1.50362i
\(431\) 23.7265i 1.14287i −0.820649 0.571433i \(-0.806388\pi\)
0.820649 0.571433i \(-0.193612\pi\)
\(432\) 9.24660i 0.444877i
\(433\) 28.1276i 1.35172i 0.737028 + 0.675862i \(0.236228\pi\)
−0.737028 + 0.675862i \(0.763772\pi\)
\(434\) −18.0573 + 3.29474i −0.866780 + 0.158152i
\(435\) 6.49479i 0.311401i
\(436\) 10.5786i 0.506623i
\(437\) 16.3189 0.780639
\(438\) −11.8031 −0.563975
\(439\) 16.7754 0.800648 0.400324 0.916374i \(-0.368898\pi\)
0.400324 + 0.916374i \(0.368898\pi\)
\(440\) 23.3687 + 5.24660i 1.11406 + 0.250122i
\(441\) −6.54893 + 2.47214i −0.311854 + 0.117721i
\(442\) 67.6236i 3.21653i
\(443\) 11.1985 0.532055 0.266028 0.963965i \(-0.414289\pi\)
0.266028 + 0.963965i \(0.414289\pi\)
\(444\) 12.7263i 0.603965i
\(445\) −0.418895 −0.0198575
\(446\) −5.12183 −0.242526
\(447\) −16.8456 −0.796767
\(448\) 17.0652 3.11371i 0.806255 0.147109i
\(449\) 7.48810 0.353385 0.176693 0.984266i \(-0.443460\pi\)
0.176693 + 0.984266i \(0.443460\pi\)
\(450\) 2.60278i 0.122696i
\(451\) 27.0892 + 6.08191i 1.27558 + 0.286386i
\(452\) 28.6831 1.34914
\(453\) −16.7907 −0.788896
\(454\) 4.17817i 0.196091i
\(455\) 2.88344 + 15.8031i 0.135178 + 0.740862i
\(456\) −20.4078 −0.955683
\(457\) 35.4188i 1.65682i 0.560122 + 0.828410i \(0.310754\pi\)
−0.560122 + 0.828410i \(0.689246\pi\)
\(458\) −23.5609 −1.10093
\(459\) 4.27913i 0.199733i
\(460\) 27.5700i 1.28546i
\(461\) −3.80732 −0.177324 −0.0886622 0.996062i \(-0.528259\pi\)
−0.0886622 + 0.996062i \(0.528259\pi\)
\(462\) −22.8207 0.921939i −1.06171 0.0428925i
\(463\) −19.4164 −0.902357 −0.451178 0.892434i \(-0.648996\pi\)
−0.451178 + 0.892434i \(0.648996\pi\)
\(464\) 60.0547i 2.78797i
\(465\) 2.66550i 0.123610i
\(466\) 19.2947 0.893811
\(467\) 31.1400i 1.44099i 0.693461 + 0.720494i \(0.256085\pi\)
−0.693461 + 0.720494i \(0.743915\pi\)
\(468\) −28.9888 −1.34001
\(469\) −7.60845 + 1.38824i −0.351326 + 0.0641028i
\(470\) 32.9655i 1.52059i
\(471\) −5.04463 −0.232444
\(472\) 35.3197 1.62572
\(473\) 8.70355 38.7662i 0.400190 1.78247i
\(474\) 19.3158i 0.887204i
\(475\) −2.82604 −0.129668
\(476\) −53.1763 + 9.70253i −2.43733 + 0.444715i
\(477\) 13.1055 0.600058
\(478\) −19.9813 −0.913924
\(479\) −41.3914 −1.89122 −0.945610 0.325302i \(-0.894534\pi\)
−0.945610 + 0.325302i \(0.894534\pi\)
\(480\) 9.62422i 0.439284i
\(481\) −16.1839 −0.737924
\(482\) 35.4094i 1.61285i
\(483\) 2.74231 + 15.0297i 0.124779 + 0.683874i
\(484\) −47.4786 22.4509i −2.15812 1.02050i
\(485\) −2.43997 −0.110793
\(486\) 2.60278 0.118065
\(487\) 31.4585 1.42552 0.712761 0.701407i \(-0.247444\pi\)
0.712761 + 0.701407i \(0.247444\pi\)
\(488\) 56.7895i 2.57074i
\(489\) 16.9045i 0.764448i
\(490\) −17.0454 + 6.43443i −0.770035 + 0.290678i
\(491\) 14.2888i 0.644845i −0.946596 0.322422i \(-0.895503\pi\)
0.946596 0.322422i \(-0.104497\pi\)
\(492\) 39.9672i 1.80186i
\(493\) 27.7920i 1.25169i
\(494\) 44.6603i 2.00936i
\(495\) 0.726543 3.23607i 0.0326557 0.145450i
\(496\) 24.6468i 1.10667i
\(497\) 28.9888 5.28929i 1.30033 0.237257i
\(498\) 24.2507 1.08670
\(499\) 16.9729 0.759813 0.379907 0.925025i \(-0.375956\pi\)
0.379907 + 0.925025i \(0.375956\pi\)
\(500\) 4.77447i 0.213521i
\(501\) 6.32283i 0.282483i
\(502\) 57.1486 2.55066
\(503\) −24.3271 −1.08469 −0.542347 0.840155i \(-0.682464\pi\)
−0.542347 + 0.840155i \(0.682464\pi\)
\(504\) −3.42943 18.7955i −0.152759 0.837220i
\(505\) 6.15537i 0.273910i
\(506\) −10.9197 + 48.6370i −0.485440 + 2.16218i
\(507\) 23.8647i 1.05987i
\(508\) 4.82300i 0.213986i
\(509\) 42.7211i 1.89358i −0.321852 0.946790i \(-0.604305\pi\)
0.321852 0.946790i \(-0.395695\pi\)
\(510\) 11.1376i 0.493183i
\(511\) 11.8031 2.15360i 0.522140 0.0952695i
\(512\) 44.5542i 1.96904i
\(513\) 2.82604i 0.124773i
\(514\) 10.4020 0.458812
\(515\) 13.1300 0.578579
\(516\) 57.1953 2.51788
\(517\) 9.20202 40.9864i 0.404705 1.80258i
\(518\) −3.29474 18.0573i −0.144762 0.793394i
\(519\) 8.78248i 0.385508i
\(520\) −43.8453 −1.92274
\(521\) 4.33936i 0.190111i 0.995472 + 0.0950555i \(0.0303029\pi\)
−0.995472 + 0.0950555i \(0.969697\pi\)
\(522\) −16.9045 −0.739890
\(523\) 9.34869 0.408790 0.204395 0.978889i \(-0.434477\pi\)
0.204395 + 0.978889i \(0.434477\pi\)
\(524\) 97.1066 4.24212
\(525\) −0.474903 2.60278i −0.0207265 0.113595i
\(526\) −27.1189 −1.18244
\(527\) 11.4060i 0.496854i
\(528\) 6.71805 29.9226i 0.292366 1.30222i
\(529\) 10.3445 0.449760
\(530\) 34.1106 1.48167
\(531\) 4.89103i 0.212253i
\(532\) 35.1189 6.40779i 1.52260 0.277813i
\(533\) −50.8258 −2.20151
\(534\) 1.09029i 0.0471815i
\(535\) −10.1032 −0.436798
\(536\) 21.1094i 0.911787i
\(537\) 11.1224i 0.479969i
\(538\) 57.8544 2.49428
\(539\) 22.9889 3.24192i 0.990202 0.139639i
\(540\) 4.77447 0.205460
\(541\) 26.1745i 1.12533i 0.826685 + 0.562664i \(0.190224\pi\)
−0.826685 + 0.562664i \(0.809776\pi\)
\(542\) 11.8640i 0.509601i
\(543\) −8.49321 −0.364478
\(544\) 41.1833i 1.76572i
\(545\) −2.21566 −0.0949084
\(546\) 41.1321 7.50495i 1.76029 0.321182i
\(547\) 7.28713i 0.311575i −0.987791 0.155788i \(-0.950208\pi\)
0.987791 0.155788i \(-0.0497916\pi\)
\(548\) 45.9989 1.96497
\(549\) 7.86414 0.335633
\(550\) 1.89103 8.42278i 0.0806338 0.359148i
\(551\) 18.3546i 0.781930i
\(552\) −41.6993 −1.77484
\(553\) −3.52436 19.3158i −0.149871 0.821392i
\(554\) 47.0437 1.99870
\(555\) 2.66550 0.113144
\(556\) 14.7136 0.623997
\(557\) 9.67553i 0.409965i 0.978766 + 0.204983i \(0.0657138\pi\)
−0.978766 + 0.204983i \(0.934286\pi\)
\(558\) −6.93771 −0.293697
\(559\) 72.7346i 3.07635i
\(560\) −4.39124 24.0669i −0.185564 1.01701i
\(561\) −3.10897 + 13.8476i −0.131261 + 0.584644i
\(562\) 33.2254 1.40153
\(563\) 3.97478 0.167517 0.0837586 0.996486i \(-0.473308\pi\)
0.0837586 + 0.996486i \(0.473308\pi\)
\(564\) 60.4710 2.54629
\(565\) 6.00759i 0.252741i
\(566\) 33.1552i 1.39362i
\(567\) −2.60278 + 0.474903i −0.109307 + 0.0199440i
\(568\) 80.4285i 3.37471i
\(569\) 19.1962i 0.804746i −0.915476 0.402373i \(-0.868186\pi\)
0.915476 0.402373i \(-0.131814\pi\)
\(570\) 7.35557i 0.308091i
\(571\) 17.4974i 0.732244i 0.930567 + 0.366122i \(0.119315\pi\)
−0.930567 + 0.366122i \(0.880685\pi\)
\(572\) 93.8098 + 21.0616i 3.92238 + 0.880630i
\(573\) 25.1189i 1.04936i
\(574\) −10.3472 56.7092i −0.431882 2.36700i
\(575\) −5.77447 −0.240812
\(576\) 6.55653 0.273189
\(577\) 25.7540i 1.07215i −0.844170 0.536076i \(-0.819906\pi\)
0.844170 0.536076i \(-0.180094\pi\)
\(578\) 3.41210i 0.141925i
\(579\) −5.20556 −0.216336
\(580\) −31.0091 −1.28758
\(581\) −24.2507 + 4.42478i −1.00609 + 0.183571i
\(582\) 6.35069i 0.263245i
\(583\) −42.4102 9.52168i −1.75645 0.394348i
\(584\) 32.7474i 1.35510i
\(585\) 6.07163i 0.251031i
\(586\) 36.4686i 1.50651i
\(587\) 30.8343i 1.27267i 0.771414 + 0.636334i \(0.219550\pi\)
−0.771414 + 0.636334i \(0.780450\pi\)
\(588\) 11.8031 + 31.2677i 0.486753 + 1.28946i
\(589\) 7.53281i 0.310384i
\(590\) 12.7303i 0.524097i
\(591\) −14.1068 −0.580278
\(592\) 24.6468 1.01298
\(593\) 11.6886 0.479995 0.239998 0.970773i \(-0.422853\pi\)
0.239998 + 0.970773i \(0.422853\pi\)
\(594\) −8.42278 1.89103i −0.345591 0.0775899i
\(595\) 2.03217 + 11.1376i 0.0833109 + 0.456598i
\(596\) 80.4285i 3.29448i
\(597\) 0.217938 0.00891962
\(598\) 91.2547i 3.73168i
\(599\) 23.7879 0.971949 0.485975 0.873973i \(-0.338465\pi\)
0.485975 + 0.873973i \(0.338465\pi\)
\(600\) 7.22133 0.294810
\(601\) 27.3449 1.11542 0.557711 0.830035i \(-0.311680\pi\)
0.557711 + 0.830035i \(0.311680\pi\)
\(602\) −81.1541 + 14.8074i −3.30759 + 0.603503i
\(603\) −2.92320 −0.119042
\(604\) 80.1667i 3.26194i
\(605\) −4.70228 + 9.94427i −0.191175 + 0.404292i
\(606\) 16.0211 0.650812
\(607\) 35.8698 1.45591 0.727955 0.685625i \(-0.240471\pi\)
0.727955 + 0.685625i \(0.240471\pi\)
\(608\) 27.1985i 1.10304i
\(609\) 16.9045 3.08439i 0.685005 0.124986i
\(610\) 20.4686 0.828751
\(611\) 76.9003i 3.11105i
\(612\) −20.4306 −0.825856
\(613\) 30.6661i 1.23859i −0.785157 0.619297i \(-0.787418\pi\)
0.785157 0.619297i \(-0.212582\pi\)
\(614\) 21.5489i 0.869644i
\(615\) 8.37103 0.337552
\(616\) −2.55789 + 63.3153i −0.103060 + 2.55104i
\(617\) −12.1325 −0.488437 −0.244219 0.969720i \(-0.578531\pi\)
−0.244219 + 0.969720i \(0.578531\pi\)
\(618\) 34.1746i 1.37470i
\(619\) 14.1708i 0.569573i 0.958591 + 0.284787i \(0.0919228\pi\)
−0.958591 + 0.284787i \(0.908077\pi\)
\(620\) −12.7263 −0.511102
\(621\) 5.77447i 0.231721i
\(622\) 28.7078 1.15108
\(623\) −0.198934 1.09029i −0.00797014 0.0436816i
\(624\) 56.1420i 2.24748i
\(625\) 1.00000 0.0400000
\(626\) −18.9424 −0.757091
\(627\) 2.05324 9.14527i 0.0819985 0.365227i
\(628\) 24.0854i 0.961113i
\(629\) −11.4060 −0.454787
\(630\) −6.77447 + 1.23607i −0.269901 + 0.0492461i
\(631\) −21.9815 −0.875072 −0.437536 0.899201i \(-0.644149\pi\)
−0.437536 + 0.899201i \(0.644149\pi\)
\(632\) 53.5911 2.13174
\(633\) 26.5392 1.05484
\(634\) 22.6184i 0.898290i
\(635\) 1.01017 0.0400872
\(636\) 62.5716i 2.48113i
\(637\) −39.7627 + 15.0099i −1.57546 + 0.594714i
\(638\) 54.7041 + 12.2818i 2.16576 + 0.486243i
\(639\) 11.1376 0.440598
\(640\) −2.18323 −0.0862999
\(641\) −31.3462 −1.23810 −0.619050 0.785352i \(-0.712482\pi\)
−0.619050 + 0.785352i \(0.712482\pi\)
\(642\) 26.2963i 1.03783i
\(643\) 33.2517i 1.31132i −0.755057 0.655660i \(-0.772391\pi\)
0.755057 0.655660i \(-0.227609\pi\)
\(644\) 71.7587 13.0931i 2.82769 0.515939i
\(645\) 11.9794i 0.471689i
\(646\) 31.4754i 1.23838i
\(647\) 37.8242i 1.48702i 0.668723 + 0.743511i \(0.266841\pi\)
−0.668723 + 0.743511i \(0.733159\pi\)
\(648\) 7.22133i 0.283681i
\(649\) −3.55354 + 15.8277i −0.139489 + 0.621292i
\(650\) 15.8031i 0.619850i
\(651\) 6.93771 1.26585i 0.271910 0.0496127i
\(652\) 80.7100 3.16085
\(653\) −36.1612 −1.41510 −0.707548 0.706665i \(-0.750199\pi\)
−0.707548 + 0.706665i \(0.750199\pi\)
\(654\) 5.76687i 0.225503i
\(655\) 20.3387i 0.794700i
\(656\) 77.4036 3.02210
\(657\) 4.53482 0.176920
\(658\) −85.8020 + 15.6554i −3.34491 + 0.610312i
\(659\) 0.553632i 0.0215665i −0.999942 0.0107832i \(-0.996568\pi\)
0.999942 0.0107832i \(-0.00343248\pi\)
\(660\) −15.4505 3.46885i −0.601410 0.135025i
\(661\) 7.29711i 0.283825i 0.989879 + 0.141912i \(0.0453251\pi\)
−0.989879 + 0.141912i \(0.954675\pi\)
\(662\) 44.8667i 1.74379i
\(663\) 25.9813i 1.00903i
\(664\) 67.2828i 2.61108i
\(665\) −1.34210 7.35557i −0.0520443 0.285237i
\(666\) 6.93771i 0.268831i
\(667\) 37.5039i 1.45216i
\(668\) 30.1882 1.16801
\(669\) 1.96783 0.0760807
\(670\) −7.60845 −0.293940
\(671\) −25.4489 5.71363i −0.982444 0.220572i
\(672\) −25.0497 + 4.57057i −0.966315 + 0.176314i
\(673\) 8.61671i 0.332150i −0.986113 0.166075i \(-0.946891\pi\)
0.986113 0.166075i \(-0.0531093\pi\)
\(674\) 13.2702 0.511147
\(675\) 1.00000i 0.0384900i
\(676\) −113.941 −4.38236
\(677\) −14.1483 −0.543764 −0.271882 0.962331i \(-0.587646\pi\)
−0.271882 + 0.962331i \(0.587646\pi\)
\(678\) −15.6365 −0.600514
\(679\) −1.15875 6.35069i −0.0444686 0.243717i
\(680\) −30.9010 −1.18500
\(681\) 1.60527i 0.0615142i
\(682\) 22.4509 + 5.04054i 0.859689 + 0.193012i
\(683\) −40.0141 −1.53110 −0.765548 0.643379i \(-0.777532\pi\)
−0.765548 + 0.643379i \(0.777532\pi\)
\(684\) 13.4929 0.515912
\(685\) 9.63435i 0.368109i
\(686\) −24.8423 41.3098i −0.948485 1.57722i
\(687\) 9.05222 0.345364
\(688\) 110.769i 4.22302i
\(689\) 79.5716 3.03144
\(690\) 15.0297i 0.572170i
\(691\) 0.111456i 0.00423999i 0.999998 + 0.00212000i \(0.000674816\pi\)
−0.999998 + 0.00212000i \(0.999325\pi\)
\(692\) −41.9316 −1.59400
\(693\) 8.76781 + 0.354213i 0.333062 + 0.0134554i
\(694\) 12.0514 0.457467
\(695\) 3.08173i 0.116897i
\(696\) 46.9010i 1.77778i
\(697\) −35.8207 −1.35681
\(698\) 37.0683i 1.40306i
\(699\) −7.41312 −0.280390
\(700\) −12.4269 + 2.26741i −0.469692 + 0.0857000i
\(701\) 2.90978i 0.109901i −0.998489 0.0549504i \(-0.982500\pi\)
0.998489 0.0549504i \(-0.0175001\pi\)
\(702\) 15.8031 0.596451
\(703\) 7.53281 0.284105
\(704\) −21.2174 4.76360i −0.799660 0.179535i
\(705\) 12.6655i 0.477010i
\(706\) 33.2518 1.25145
\(707\) −16.0211 + 2.92320i −0.602534 + 0.109938i
\(708\) −23.3521 −0.877624
\(709\) 26.1351 0.981526 0.490763 0.871293i \(-0.336718\pi\)
0.490763 + 0.871293i \(0.336718\pi\)
\(710\) 28.9888 1.08793
\(711\) 7.42122i 0.278317i
\(712\) 3.02498 0.113366
\(713\) 15.3918i 0.576429i
\(714\) 28.9888 5.28929i 1.08488 0.197947i
\(715\) 4.41130 19.6482i 0.164973 0.734802i
\(716\) 53.1038 1.98458
\(717\) 7.67691 0.286699
\(718\) 43.4238 1.62056
\(719\) 3.27979i 0.122316i −0.998128 0.0611578i \(-0.980521\pi\)
0.998128 0.0611578i \(-0.0194793\pi\)
\(720\) 9.24660i 0.344601i
\(721\) 6.23549 + 34.1746i 0.232222 + 1.27273i
\(722\) 28.6657i 1.06683i
\(723\) 13.6044i 0.505955i
\(724\) 40.5505i 1.50705i
\(725\) 6.49479i 0.241210i
\(726\) 25.8828 + 12.2390i 0.960599 + 0.454232i
\(727\) 1.98302i 0.0735461i 0.999324 + 0.0367730i \(0.0117079\pi\)
−0.999324 + 0.0367730i \(0.988292\pi\)
\(728\) −20.8222 114.120i −0.771724 4.22955i
\(729\) −1.00000 −0.0370370
\(730\) 11.8031 0.436854
\(731\) 51.2614i 1.89597i
\(732\) 37.5471i 1.38778i
\(733\) 1.56571 0.0578308 0.0289154 0.999582i \(-0.490795\pi\)
0.0289154 + 0.999582i \(0.490795\pi\)
\(734\) −73.4711 −2.71187
\(735\) 6.54893 2.47214i 0.241561 0.0911861i
\(736\) 55.5747i 2.04851i
\(737\) 9.45968 + 2.12383i 0.348452 + 0.0782323i
\(738\) 21.7879i 0.802025i
\(739\) 29.6758i 1.09164i −0.837902 0.545820i \(-0.816218\pi\)
0.837902 0.545820i \(-0.183782\pi\)
\(740\) 12.7263i 0.467829i
\(741\) 17.1587i 0.630341i
\(742\) 16.1992 + 88.7825i 0.594693 + 3.25931i
\(743\) 41.8830i 1.53654i −0.640127 0.768269i \(-0.721118\pi\)
0.640127 0.768269i \(-0.278882\pi\)
\(744\) 19.2484i 0.705682i
\(745\) 16.8456 0.617173
\(746\) −25.7786 −0.943820
\(747\) −9.31722 −0.340899
\(748\) 66.1147 + 14.8437i 2.41739 + 0.542738i
\(749\) −4.79802 26.2963i −0.175316 0.960847i
\(750\) 2.60278i 0.0950401i
\(751\) 1.81073 0.0660744 0.0330372 0.999454i \(-0.489482\pi\)
0.0330372 + 0.999454i \(0.489482\pi\)
\(752\) 117.113i 4.27067i
\(753\) −21.9567 −0.800148
\(754\) −102.638 −3.73785
\(755\) 16.7907 0.611076
\(756\) 2.26741 + 12.4269i 0.0824648 + 0.451962i
\(757\) −39.7295 −1.44399 −0.721996 0.691897i \(-0.756775\pi\)
−0.721996 + 0.691897i \(0.756775\pi\)
\(758\) 67.0122i 2.43399i
\(759\) 4.19540 18.6866i 0.152283 0.678279i
\(760\) 20.4078 0.740269
\(761\) 33.5623 1.21663 0.608316 0.793695i \(-0.291845\pi\)
0.608316 + 0.793695i \(0.291845\pi\)
\(762\) 2.62924i 0.0952473i
\(763\) −1.05222 5.76687i −0.0380930 0.208775i
\(764\) 119.930 4.33890
\(765\) 4.27913i 0.154712i
\(766\) −27.3602 −0.988563
\(767\) 29.6966i 1.07228i
\(768\) 18.7955i 0.678226i
\(769\) 16.3289 0.588835 0.294418 0.955677i \(-0.404874\pi\)
0.294418 + 0.955677i \(0.404874\pi\)
\(770\) 22.8207 + 0.921939i 0.822401 + 0.0332244i
\(771\) −3.99649 −0.143930
\(772\) 24.8538i 0.894507i
\(773\) 18.0913i 0.650699i −0.945594 0.325349i \(-0.894518\pi\)
0.945594 0.325349i \(-0.105482\pi\)
\(774\) −31.1798 −1.12073
\(775\) 2.66550i 0.0957475i
\(776\) 17.6198 0.632514
\(777\) 1.26585 + 6.93771i 0.0454122 + 0.248889i
\(778\) 45.3951i 1.62749i
\(779\) 23.6569 0.847596
\(780\) 28.9888 1.03797
\(781\) −36.0421 8.09196i −1.28969 0.289553i
\(782\) 64.3139i 2.29986i
\(783\) 6.49479 0.232105
\(784\) 60.5554 22.8589i 2.16269 0.816388i
\(785\) 5.04463 0.180050
\(786\) −52.9373 −1.88821
\(787\) −5.83044 −0.207833 −0.103916 0.994586i \(-0.533137\pi\)
−0.103916 + 0.994586i \(0.533137\pi\)
\(788\) 67.3527i 2.39934i
\(789\) 10.4192 0.370934
\(790\) 19.3158i 0.687226i
\(791\) 15.6365 2.85302i 0.555968 0.101442i
\(792\) −5.24660 + 23.3687i −0.186430 + 0.830371i
\(793\) 47.7482 1.69559
\(794\) −31.2487 −1.10897
\(795\) −13.1055 −0.464803
\(796\) 1.04054i 0.0368809i
\(797\) 15.2515i 0.540235i −0.962827 0.270117i \(-0.912938\pi\)
0.962827 0.270117i \(-0.0870625\pi\)
\(798\) −19.1449 + 3.49318i −0.677724 + 0.123657i
\(799\) 54.1973i 1.91736i
\(800\) 9.62422i 0.340268i
\(801\) 0.418895i 0.0148009i
\(802\) 37.9641i 1.34056i
\(803\) −14.6750 3.29474i −0.517869 0.116269i
\(804\) 13.9567i 0.492216i
\(805\) −2.74231 15.0297i −0.0966538 0.529726i
\(806\) −42.1232 −1.48373
\(807\) −22.2279 −0.782459
\(808\) 44.4499i 1.56374i
\(809\) 9.95650i 0.350052i 0.984564 + 0.175026i \(0.0560009\pi\)
−0.984564 + 0.175026i \(0.943999\pi\)
\(810\) −2.60278 −0.0914524
\(811\) −42.0271 −1.47577 −0.737885 0.674927i \(-0.764175\pi\)
−0.737885 + 0.674927i \(0.764175\pi\)
\(812\) −14.7263 80.7100i −0.516793 2.83237i
\(813\) 4.55819i 0.159863i
\(814\) −5.04054 + 22.4509i −0.176671 + 0.786903i
\(815\) 16.9045i 0.592139i
\(816\) 39.5674i 1.38514i
\(817\) 33.8543i 1.18441i
\(818\) 22.1276i 0.773672i
\(819\) −15.8031 + 2.88344i −0.552206 + 0.100755i
\(820\) 39.9672i 1.39571i
\(821\) 12.0729i 0.421347i 0.977556 + 0.210674i \(0.0675657\pi\)
−0.977556 + 0.210674i \(0.932434\pi\)
\(822\) −25.0761 −0.874629
\(823\) 27.6005 0.962092 0.481046 0.876695i \(-0.340257\pi\)
0.481046 + 0.876695i \(0.340257\pi\)
\(824\) −94.8163 −3.30308
\(825\) −0.726543 + 3.23607i −0.0252950 + 0.112665i
\(826\) 33.1341 6.04565i 1.15288 0.210355i
\(827\) 9.74038i 0.338706i 0.985555 + 0.169353i \(0.0541678\pi\)
−0.985555 + 0.169353i \(0.945832\pi\)
\(828\) 27.5700 0.958124
\(829\) 0.606700i 0.0210716i 0.999944 + 0.0105358i \(0.00335370\pi\)
−0.999944 + 0.0105358i \(0.996646\pi\)
\(830\) −24.2507 −0.841754
\(831\) −18.0744 −0.626995
\(832\) 39.8088 1.38012
\(833\) −28.0237 + 10.5786i −0.970965 + 0.366526i
\(834\) −8.02107 −0.277747
\(835\) 6.32283i 0.218811i
\(836\) −43.6638 9.80313i −1.51014 0.339048i
\(837\) 2.66550 0.0921331
\(838\) −63.6119 −2.19744
\(839\) 43.5378i 1.50309i −0.659680 0.751546i \(-0.729308\pi\)
0.659680 0.751546i \(-0.270692\pi\)
\(840\) 3.42943 + 18.7955i 0.118327 + 0.648508i
\(841\) −13.1823 −0.454561
\(842\) 59.4768i 2.04971i
\(843\) −12.7654 −0.439662
\(844\) 126.710i 4.36155i
\(845\) 23.8647i 0.820972i
\(846\) −32.9655 −1.13338
\(847\) −28.1159 7.51645i −0.966073 0.258268i
\(848\) −121.181 −4.16137
\(849\) 12.7384i 0.437180i
\(850\) 11.1376i 0.382018i
\(851\) 15.3918 0.527625
\(852\) 53.1763i 1.82179i
\(853\) 8.69683 0.297774 0.148887 0.988854i \(-0.452431\pi\)
0.148887 + 0.988854i \(0.452431\pi\)
\(854\) 9.72061 + 53.2754i 0.332632 + 1.82305i
\(855\) 2.82604i 0.0966487i
\(856\) 72.9583 2.49366
\(857\) 9.39456 0.320912 0.160456 0.987043i \(-0.448704\pi\)
0.160456 + 0.987043i \(0.448704\pi\)
\(858\) −51.1400 11.4816i −1.74589 0.391977i
\(859\) 18.3701i 0.626779i −0.949625 0.313389i \(-0.898536\pi\)
0.949625 0.313389i \(-0.101464\pi\)
\(860\) −57.1953 −1.95034
\(861\) 3.97542 + 21.7879i 0.135482 + 0.742531i
\(862\) 61.7549 2.10338
\(863\) 16.8723 0.574341 0.287171 0.957879i \(-0.407285\pi\)
0.287171 + 0.957879i \(0.407285\pi\)
\(864\) −9.62422 −0.327423
\(865\) 8.78248i 0.298613i
\(866\) −73.2099 −2.48777
\(867\) 1.31094i 0.0445220i
\(868\) −6.04377 33.1239i −0.205139 1.12430i
\(869\) −5.39183 + 24.0156i −0.182905 + 0.814672i
\(870\) 16.9045 0.573116
\(871\) −17.7486 −0.601389
\(872\) 16.0000 0.541828
\(873\) 2.43997i 0.0825803i
\(874\) 42.4745i 1.43672i
\(875\) 0.474903 + 2.60278i 0.0160546 + 0.0879900i
\(876\) 21.6513i 0.731531i
\(877\) 18.5832i 0.627511i 0.949504 + 0.313755i \(0.101587\pi\)
−0.949504 + 0.313755i \(0.898413\pi\)
\(878\) 43.6628i 1.47355i
\(879\) 14.0114i 0.472593i
\(880\) −6.71805 + 29.9226i −0.226465 + 1.00869i
\(881\) 10.1366i 0.341511i −0.985313 0.170756i \(-0.945379\pi\)
0.985313 0.170756i \(-0.0546209\pi\)
\(882\) −6.43443 17.0454i −0.216658 0.573950i
\(883\) −21.6343 −0.728054 −0.364027 0.931388i \(-0.618598\pi\)
−0.364027 + 0.931388i \(0.618598\pi\)
\(884\) −124.047 −4.17215
\(885\) 4.89103i 0.164410i
\(886\) 29.1472i 0.979218i
\(887\) 17.5316 0.588653 0.294326 0.955705i \(-0.404905\pi\)
0.294326 + 0.955705i \(0.404905\pi\)
\(888\) −19.2484 −0.645935
\(889\) 0.479730 + 2.62924i 0.0160896 + 0.0881818i
\(890\) 1.09029i 0.0365467i
\(891\) 3.23607 + 0.726543i 0.108412 + 0.0243401i
\(892\) 9.39534i 0.314579i
\(893\) 35.7933i 1.19778i
\(894\) 43.8453i 1.46641i
\(895\) 11.1224i 0.371782i
\(896\) −1.03682 5.68248i −0.0346379 0.189838i
\(897\) 35.0605i 1.17063i
\(898\) 19.4899i 0.650386i
\(899\) −17.3118 −0.577382
\(900\) −4.77447 −0.159149
\(901\) 56.0800 1.86829
\(902\) −15.8299 + 70.5073i −0.527077 + 2.34764i
\(903\) 31.1798 5.68906i 1.03760 0.189320i
\(904\) 43.3828i 1.44289i
\(905\) 8.49321 0.282324
\(906\) 43.7025i 1.45192i
\(907\) 25.4469 0.844949 0.422475 0.906375i \(-0.361162\pi\)
0.422475 + 0.906375i \(0.361162\pi\)
\(908\) −7.66432 −0.254349
\(909\) −6.15537 −0.204161
\(910\) −41.1321 + 7.50495i −1.36352 + 0.248787i
\(911\) 16.7205 0.553973 0.276987 0.960874i \(-0.410664\pi\)
0.276987 + 0.960874i \(0.410664\pi\)
\(912\) 26.1313i 0.865294i
\(913\) 30.1512 + 6.76936i 0.997858 + 0.224033i
\(914\) −92.1873 −3.04928
\(915\) −7.86414 −0.259980
\(916\) 43.2195i 1.42801i
\(917\) 52.9373 9.65892i 1.74814 0.318966i
\(918\) 11.1376 0.367597
\(919\) 3.01777i 0.0995469i −0.998761 0.0497734i \(-0.984150\pi\)
0.998761 0.0497734i \(-0.0158499\pi\)
\(920\) 41.6993 1.37479
\(921\) 8.27920i 0.272809i
\(922\) 9.90961i 0.326356i
\(923\) 67.6236 2.22586
\(924\) 1.69118 41.8616i 0.0556357 1.37715i
\(925\) −2.66550 −0.0876410
\(926\) 50.5367i 1.66074i
\(927\) 13.1300i 0.431247i
\(928\) 62.5073 2.05190
\(929\) 44.3174i 1.45401i 0.686634 + 0.727004i \(0.259088\pi\)
−0.686634 + 0.727004i \(0.740912\pi\)
\(930\) 6.93771 0.227496
\(931\) 18.5076 6.98636i 0.606561 0.228969i
\(932\) 35.3937i 1.15936i
\(933\) −11.0297 −0.361096
\(934\) −81.0506 −2.65206
\(935\) 3.10897 13.8476i 0.101674 0.452863i
\(936\) 43.8453i 1.43313i
\(937\) −55.4748 −1.81228 −0.906142 0.422974i \(-0.860986\pi\)
−0.906142 + 0.422974i \(0.860986\pi\)
\(938\) −3.61328 19.8031i −0.117978 0.646595i
\(939\) 7.27776 0.237501
\(940\) −60.4710 −1.97235
\(941\) −56.3860 −1.83813 −0.919065 0.394106i \(-0.871054\pi\)
−0.919065 + 0.394106i \(0.871054\pi\)
\(942\) 13.1301i 0.427800i
\(943\) 48.3382 1.57411
\(944\) 45.2254i 1.47196i
\(945\) 2.60278 0.474903i 0.0846685 0.0154486i
\(946\) 100.900 + 22.6534i 3.28054 + 0.736527i
\(947\) −26.7831 −0.870333 −0.435167 0.900350i \(-0.643311\pi\)
−0.435167 + 0.900350i \(0.643311\pi\)
\(948\) −35.4324 −1.15079
\(949\) 27.5337 0.893783
\(950\) 7.35557i 0.238646i
\(951\) 8.69007i 0.281795i
\(952\) −14.6750 80.4285i −0.475619 2.60670i
\(953\) 26.0197i 0.842861i 0.906861 + 0.421431i \(0.138472\pi\)
−0.906861 + 0.421431i \(0.861528\pi\)
\(954\) 34.1106i 1.10437i
\(955\) 25.1189i 0.812830i
\(956\) 36.6531i 1.18545i
\(957\) −21.0176 4.71874i −0.679402 0.152535i
\(958\) 107.733i 3.48069i
\(959\) 25.0761 4.57538i 0.809749 0.147747i
\(960\) −6.55653 −0.211611
\(961\) 23.8951 0.770810
\(962\) 42.1232i 1.35811i
\(963\) 10.1032i 0.325570i
\(964\) −64.9540 −2.09203
\(965\) 5.20556 0.167573
\(966\) −39.1189 + 7.13763i −1.25863 + 0.229650i
\(967\) 22.6715i 0.729066i 0.931190 + 0.364533i \(0.118771\pi\)
−0.931190 + 0.364533i \(0.881229\pi\)
\(968\) 33.9567 71.8109i 1.09141 2.30809i
\(969\) 12.0930i 0.388483i
\(970\) 6.35069i 0.203909i
\(971\) 16.5616i 0.531488i −0.964044 0.265744i \(-0.914382\pi\)
0.964044 0.265744i \(-0.0856176\pi\)
\(972\) 4.77447i 0.153141i
\(973\) 8.02107 1.46352i 0.257144 0.0469184i
\(974\) 81.8797i 2.62359i
\(975\) 6.07163i 0.194448i
\(976\) −72.7166 −2.32760
\(977\) 2.81501 0.0900600 0.0450300 0.998986i \(-0.485662\pi\)
0.0450300 + 0.998986i \(0.485662\pi\)
\(978\) −43.9987 −1.40692
\(979\) −0.304345 + 1.35557i −0.00972691 + 0.0433243i
\(980\) −11.8031 31.2677i −0.377037 0.998809i
\(981\) 2.21566i 0.0707405i
\(982\) 37.1906 1.18680
\(983\) 53.1572i 1.69545i −0.530434 0.847726i \(-0.677971\pi\)
0.530434 0.847726i \(-0.322029\pi\)
\(984\) −60.4499 −1.92707
\(985\) 14.1068 0.449481
\(986\) −72.3366 −2.30367
\(987\) 32.9655 6.01488i 1.04930 0.191456i
\(988\) 81.9237 2.60634
\(989\) 69.1747i 2.19963i
\(990\) 8.42278 + 1.89103i 0.267693 + 0.0601009i
\(991\) 3.92919 0.124815 0.0624075 0.998051i \(-0.480122\pi\)
0.0624075 + 0.998051i \(0.480122\pi\)
\(992\) 25.6533 0.814494
\(993\) 17.2380i 0.547031i
\(994\) 13.7669 + 75.4515i 0.436659 + 2.39318i
\(995\) −0.217938 −0.00690911
\(996\) 44.4848i 1.40955i
\(997\) 8.49429 0.269017 0.134508 0.990912i \(-0.457054\pi\)
0.134508 + 0.990912i \(0.457054\pi\)
\(998\) 44.1768i 1.39839i
\(999\) 2.66550i 0.0843326i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1155.2.i.c.76.15 yes 16
7.6 odd 2 inner 1155.2.i.c.76.16 yes 16
11.10 odd 2 inner 1155.2.i.c.76.1 16
77.76 even 2 inner 1155.2.i.c.76.2 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.i.c.76.1 16 11.10 odd 2 inner
1155.2.i.c.76.2 yes 16 77.76 even 2 inner
1155.2.i.c.76.15 yes 16 1.1 even 1 trivial
1155.2.i.c.76.16 yes 16 7.6 odd 2 inner